Translations of Mathematical Monographs 1992; 288 pp; hardcover Volume: 99 ISBN10: 082184556X ISBN13: 9780821845561 List Price: US$120 Member Price: US$96 Order Code: MMONO/99
 This book, which originally appeared in Japanese, was written for use in an undergraduate course or first year graduate course in partial differential equations and is likely to be of interest to researchers as well. This book presents a comprehensive study of the theory of elliptic partial differential operators. Beginning with the definitions of ellipticity for higher order operators, Shimakura discusses the Laplacian in Euclidean spaces, elementary solutions, smoothness of solutions, VishikSobolev problems, the Schauder theory, and degenerate elliptic operators. The appendix covers such preliminaries as ordinary differential equations, Sobolev spaces, and maximum principles. Because elliptic operators arise in many areas, readers will appreciate this book for the way it brings together a variety of techniques that have arisen in different branches of mathematics. Readership First year graduate students specializing in partial differential equations, researchers in other fields of mathematics. Reviews "The book was designed for seniors or firstyear graduate students in Sendai specializing in elliptic partial differential equations, and will fill the same role admirably today in America or anywhere."  Mathematical Reviews "Clear, well written, interesting; although it is addressed to (undergraduate or graduate) students, it is certainly useful for partial differential equations researchers as well."  Zentralblatt MATH Table of Contents  Partial differential operators of elliptic type
 The Laplacian in Euclidean spaces
 Constructions and estimates of elementary solutions
 Smoothness of solutions
 VishikSobolev problems
 General boundary value problems
 Schauder estimates and applications
 Degenerate elliptic operators
